The lead author, Robert Hecht, an economist and former policymaker at the United Nations and the International AIDS Vaccine Initiative, predicted that by that time, poor countries would need $35 billion a year – three times what is spent now – to treat AIDS patients, care for orphans and do prevention work.

Even under the best case foreseen by the panel, more than one million people would be newly infected each year. (About 2.3 million were infected in 2007.) Achieving that outcome would cost $722 billion over 22 years, or nearly $8,000 for each infection prevented. (Condoms are cheap, but the price includes drugs that lower viral levels and prevent mother-to-child transmission.)

Their economic models assumed that condoms, drugs and circumcision would become widespread but that a microbicide and a vaccine would not.

Rapidly developing countries like Brazil, China, India, Mexico and Russia should be able to pay for fighting their own relatively small epidemics, the authors said. Southern African countries will need only some help, despite having the worlds highest AIDS rates. But much of Africa, and especially Kenya, Mozambique, Uganda and Zambia, will remain heavily dependent on donors.

Given the economic crisis, rich countries may come up with only 30 percent of what is needed; they come up with 43 percent now.